Question

एक शंकु की ऊंचाई ज्ञात कीजिए जिसका व्यास 10 सेंटीमीटर और प्रयोग ऊंचाई 13 सेंटीमीटर है​

Answer 1

$\huge{\mathbb{\red{ANSWER:-}}}$

For a Cone -

Given :-

$\sf{Diameter (d) = 10 \: cm}$

$\sf{Slant \: height (L) = 13 \: cm}$

To Find :-

$\sf{perpendicular \: height \: of \: the \: cone (h) = ?}$

Using Formula :-

$\sf{L^{2} = r^{2} + h^{2}}$

Solution :-

$\sf{radius \: of \: the \: cone =\dfrac{d}{2}}$

$\sf{r =\dfrac{10}{2} = 5 \: cm}$

By Using Formula :-

$\sf{L^{2} = r^{2} + h^{2}}$

$\sf{h^{2} = L^{2} - r^{2}}$

$\sf{h =\sqrt{L^{2} - r^{2}}}$

$\sf{h =\sqrt{13^{2} - 5^{2}}}$

$\sf{h =\sqrt{169 - 25}}$

$\sf{h =\sqrt{144}}$

$\sf{h = 12 \: cm}$

$\sf{The \: perpendicular \: height \: of \: the \: cone \: is \: 12 \: cm.}$

Short method :-

$\sf{As \: we \: know \: about \: triplets -}$

For example -

$\sf{3 , 4 , 5}$

Here ,

$\sf{3^{2} + 4^{2} = 5^{2}}$

same As -

$\sf{5 , 12 , 13}$

$\sf{8 , 15 , 17}$

$\sf{7 , 24 , 25}$

For this question -

$\sf{Using \: triplet \: is \: (5 , 12 , 13)}$

$\sf{Two \: values \: are \: 5 \: and \: 13 \: respectively .}$

$\sf{then \: , \: 3rd \: is \: surely \: 12.}$

$\sf{This \: is \: the \: answer .}$